MIT OpenCourseWare

Browse materialsMIT 18.156 · Spring 2025

Projection Theory

Subject: Mathematics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Prof. Lawrence D Guth
Term: Spring 2025
Level: Graduate
What's inside: 24 videos · 10 problem sets · 3 lecture notes · 49 other files · 2 web pages
Materials open: Videos here · files on MIT OCW

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About this course

Source: MIT OpenCourseWare 18.156 Projection Theory, Spring 2025, Prof. Lawrence D Guth — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Materials by section

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Lecture Notes

27 files

Problem Sets

1 file

18.156 (S25): Some Possible Questions to ExplorePDF Download

24 video transcripts

1 image

A diagram showing projections from three geometric shapesJPEG image Open ↗

MIT OpenCourseWare, Prof. Lawrence D Guth, 18.156 Projection Theory, Spring 2025.

License: CC BY-NC-SA 4.0 · Edition: Spring 2025 · Open the original course on OCW ↗

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Projection Theory

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Problem Sets

Lecture 01: Introduction to Projection Theory

Lecture 02: Fundamental Methods of Projection Theory

Lecture 03: Projection Theory in Euclidean Space

Lecture 04: The Fourier Method in Euclidean Space

Lecture 05: The Large Sieve

Lecture 06: Projections and Smoothing

Lecture 07: Applications of the Large Sieve to Number Theory

Lecture 08: The Szemeredi-Trotter Theorem

Lecture 09: Reflections on the Szemeredi-Trotter Theorem

Lecture 10: Sum-Product Theory

Lecture 11: Contagious Structure in Projection Theory

Lecture 12: The Bourgain-Katz-Tao Projection Theorem

Lecture 13: The Balog-Szemeredi-Gowers Theorem

Lecture 14: The Bourgain Projection Theorem Part 1 (over the Real Numbers)

Lecture 15: The Bourgain Projection Theorem, Part 2

Lecture 16: The Bourgain Projection Theorem, Part 3

Lecture 17: Random Walks on Finite Groups, Part 1

Lecture 18: Random Walks on Finite Groups, Part 2

Lecture 19: Random Walks on Finite Groups, Part 3

Lecture 20: Homogeneous Dynamics, Part 1

Lecture 21: Homogeneous Dynamics, Part 2

Lecture 22: Sharp Projection Theorems, Part 1: Introduction and Beck's Theorem.

Lecture 23: Sharp Projection Theorems, Part 2: AD Regular Case

Lecture 24: Sharp Projection Theorems, Part 3: Combining Different Scales

18.156 (S25): Problem Set 1

18.156 (S25): Problem Set 1 LaTeX Template

18.156 (S25): Problem Set 2

18.156 (S25): Problem Set 2 LaTeX Template

18.156 (S25): Problem Set 3

18.156 (S25): Problem Set 3 LaTeX Template

18.156 (S25): Problem Set 4

18.156 (S25): Problem Set 4 LaTeX Template

18.156 (S25): Problem Set 5

18.156 (S25): Problem Set 5 LaTeX Template